Inverse function

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In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by f−1. For a function f:X→Y, its inverse f−1:Y→X admits an explicit description: it sends each element y∈Y to the unique element x∈X such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the output, then divides the result by 5. Therefore, the inverse of f is the function f−1:ℝ→ℝ defined by f−1(y)=y+75.

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